Statistical shape modelling provides a powerful method to describe and compensate for physical organ shape changes, for example, due to inter-subject anatomical variation, and has been investigated extensively for a range of medical image analysis tasks, including image segmentation [1] and image registration [2]. In particular, the method originally proposed by Cootes et al. [3] in which a low-dimensional, linear statistical shape model (SSM) is constructed by applying principal component analysis (PCA) to image-based shape training data, has been applied to numerous applications where learnt information on organ shape variation provides a useful constraint or prior information. Such models help to ensure that physically implausible organ shapes are not considered, or are at least penalised, when searching for a solution within a segmentation and registration algorithm.
Variations in the shape of an organ can generally be considered as arising from two sources. The first, termed inter-subject variation, represents differences in organ shape between different people, i.e. from one person to another. Such inter-shape variation naturally arises across a population of individuals. The second, termed intra-subject variation, represents changes in the shape of an organ belonging to one person. Such intra-subject variations can be caused by many different factors, such as a change in posture of the person, natural organ motion (e.g. due to breathing or the beating heart), tissue deformation by the insertion of a medical instrument, the progression or regression of a disease, etc.
The most common use of SSMs has generally been in describing inter-subject organ shape variation within a population, where intra-subject shape variation is not explicitly considered, and where training data is acquired in a consistent way to try to ensure that the contribution of any intra-patient shape variation is minimised. SSMs that represent intra-subject organ motion may be termed statistical motion models (SMMs) to distinguish them from the more general SSM [6, 7]. One reason for this focus on inter-subject variation is that modelling subject-specific (intra-subject) organ shape variation and organ motion requires sufficient training data from an individual subject to describe statistically the range of shape variation this is difficult in practice, for example because it may require dynamic imaging data, which may be difficult or impossible to acquire, particularly if the full three-dimensional (3D) variation in organ shape is considered [1]. Particularly challenging examples include modelling non-physiological organ motion due to the intrusion or application of surgical instruments; in such circumstances, it is usually impractical and/or unethical to acquire data on organ shape changes in advance of a surgical procedure.
One approach to address this problem is to simulate organ motion using biomechanical modelling to provide synthetic training data for building a SSM [4, 5]. However, generating synthetic training data in this way is a complex and potentially time-consuming process that requires segmentation of the organ(s) of interest and computationally-intensive simulations using finite element analysis or an equivalent method. These factors place constraints on the way in which such models may be used for practical applications; for example, SMM generation using this approach is only practical as a pre-operative step in image-guided surgery applications when time is available for performing the necessary image analysis and simulations.
It is possible to build a population-based SSM using training data that is subject to both inter- and intra-subject organ shape variation, but such models are very likely to perform less effectively or efficiently compared with a subject-specific SMM for approximating subject-specific shape/motion. In particular, such models usually require additional constraints, such as that provided by an elastic model [8], to distinguish between intra- versus inter-subject variation when using the model to instantiate a shape and to prevent the generation of unrealistic or ‘over-generalised’ shape instances due to inter-subject shape variation.
The importance of distinguishing inter- and intra-subject shape variation is illustrated by considering the following: if we have first and second organ states, which each corresponds to a different organ shape that arises from intra-subject organ shape variation, then there must be some physical transition of the organ between the first and second states to produce the change in organ shape. A model of such intra-subject variation can be referred to as a SMM (statistical motion model), since the physical transition implies a motion in a general sense (including a shape change due to organ deformation) between the first and second shapes. In contrast, if the differences between the first and second organ shapes arise from inter-subject variation, then they correspond to different individuals, and there is no reason for such a physical transition to exist between the first and second shapes corresponding to some change in state. Accordingly, this type of variation is represented by a more generic SSM (statistic shape model), since the first and second shapes are not generally related to one another by motion.
If an SSM, based at least in part on inter-subject training data, is used to model subject-specific shape variations, it may permit a variation that is not, in fact, physically plausible for a given organ. As an example, it is generally possible for a human to alter the distance from the eye-line down to the lips (by movement of the lips using facial muscles); however, it is not usually possible to alter the distance or separation between the eyes, since this is determined by the (rigid) skull. On the other hand, the separation between the eyes (in effect, the skull size) does vary from one individual to another. Accordingly, an SSM which is based on at least in part on inter-subject training data might potentially allow variation in this eye separation, despite the fact that such variation is not physically plausible in the context of an individual subject.
Recently, multilinear analysis [9] has been proposed as a method for dynamic modelling of the heart [10] and cardiac valve [11] motion. This approach enables inter-subject shape variations (e.g., due to subject specific differences in the size and shape of the heart of different individuals) and intra-subject shape variations (e.g. due to physiological heart motion) to be represented by the same statistical model. However, this method requires that inter-subject temporal correspondence between motion subspaces is known—in other words, the states of the organs for different subjects must be correlated, for example, via an independent signal, such as an electrocardiographic (ECG) signal, which measures the electrical activity of the heart and is therefore is inherently correlated to its motion. Such an independent signal is very difficult to establish for organs other than the heart and lungs, i.e. for organs where a physiological signal related to motion is not available is or very difficult to measure. Furthermore, the cardiac models described in [10, 11] have demonstrated only the ability to predict organ shape at relatively few time-points from the dynamic data available over the remainder of the cardiac cycle.
In general, subject-specific dynamic data on organ motion, for example, from imaging, is often extremely limited or not available at all, but many examples exist in the context of image-guided surgical procedures where it is desirable to be able provide models which use learnt information on inter- and intra-subject organ shape variation to predict subject-specific organ shape and motion given only sparse and potentially noisy (intraoperative) spatial data that describe the current organ state.
For example, in a surgical intervention the surgeon may wish to treat or remove a particular anatomical structure or region of diseased tissue which has a specific location determined in advance of the procedure by pre-operative imaging, such as magnetic resonance imaging (MRI). However, this structure or region may be difficult to localise or not be visible using intraoperative imaging, such as ultrasound, during the procedure. Such intraoperative imaging techniques are typically low-cost, portable, and easier to utilise within a surgical procedure, but often do not provide the information of diagnostic-quality pre-operative imaging methods.
One well-established way of overcoming this difficulty is to perform a (non-rigid) registration (i.e. spatial alignment) between the pre-operative image and the intraoperative image, thereby allowing structures determined in the pre-operative images to be mapped across to (and displayed in conjunction with) the intra-operative images. In practice, this is achieved using special-purpose image fusion software, and an important requirement for surgical applications is that the image registration needs to be performed within a timescale that is acceptable in the context of the surgical procedure. To achieve a high enough accuracy to be of most clinical use, the image registration should also be able to compensate for movement and deformation in the organ or structures of surgical interest, for example, due to changes in the subject position or posture, or as a direct result of instruments used in the surgical procedure itself (for example, organ deformation arising from ultrasound imaging probe pressure). The physical nature of this organ motion in an individual subject suggests that an SMM approach is appropriate, but for cases where dynamic imaging is unavailable, generating a subject-specific SMM by performing biomechanical simulations of organ motion to provide training data is both a complex and time-consuming process, both computationally and from the point of view of implementing within a clinical workflow.